Lewis Hamilton’s 50th Formula One victory was also one of his most imperious as he beat his arch-rival Nico Rosberg into second place in Sunday’s US Grand Prix.

The fact it was also his first win for three months, since the German Grand Prix at the end of July, lent an extra zest to the podium champagne. The result cut Rosberg’s lead in the drivers’ world championship from 33 to 26 points with three races now remaining. It was Hamilton’s fourth victory in the five races that have been held here and his fifth in the US following his success in Indianapolis in 2007. Overall only Michael Schumacher (91) and Alain Prost (51) have won more races.

It was here, of course, that Hamilton clinched his third world title a year ago, a race followed by cap-throwing scenes between the two Mercedes drivers. Since then, though, Rosberg had won 12 of the following 20 races, before this one, and he remains favourite to win his first world championship.

He only has to finish at least second in Mexico, Brazil and Abu Dhabi to take the title. That is why he did not look too disconsolate in defeat here. But he knows he is up against a team-mate who appears restored to his finest form following his bad eight days in Malaysia and Japan in which he suffered an engine failure, made a dreadful start and also fell out with the media after some strange behaviour in a couple of press conferences.

It was hardly a race worthy of the glitzy billing it received but no one seemed to mind much. After successive years of declining crowds since the first race here in 2012 the figures at the Circuit of the Americas have been up this weekend, boosted by the 100,000 turnout for the Taylor Swift concert on Saturday evening.

In brilliant sunshine the atmosphere and the entire afternoon contrasted happily with last year’s monsoon conditions. The future of the Austin race – the 10th venue for Formula One in the US – has often been cause for speculation but on this showing it looks assured and there was a beaming smile on the face of Chase Carey, representing the new owners, Liberty Media.

It was not a great afternoon for everybody, however. Nico Hülkenberg was soon out of the race after being hit from behind by Valtteri Bottas. And later there were high-profile retirements in Max Verstappen (gearbox) and Kimi Raikkonen, who was told to pull over following a mishap in the pits.

There were no such dramas at the head of the field. Hamilton completed his most difficult work of the afternoon within the opening seconds of the race; he got off to a fine start. Five times this season – in Australia, Bahrain, Canada, Italy and Japan – Hamilton has made poor starts and that has cost him more dearly than his various engine failures.

But here he climbed up the steep hill towards the first corner keeping Rosberg behind him. Rosberg did have a run on his team-mate, on the outside, and at one point made a small gain on him.

But his ambitions backfired when he found himself running wide into the opening bend, allowing Daniel Ricciardo, on faster, super-soft tyres, to pass him on the inside.

By the end of the opening lap Hamilton’s lead was already 0.8sec as he maintained his fine form of the previous, pole-winning day. After that he began to stretch away, while Rosberg struggled to get past Ricciardo.

The Australian managed to get eight laps out of his extra-soft rubber before coming for a set of softs.

He returned to the field in eighth place and finished third, missing out on the chance to beat Rosberg because of the deployment of the virtual safety car when Verstappen broke down.

Despite Hamilton’s serene progress up front there were signs of confusion on the Mercedes pitwall. They told Rosberg: “We are going for the long game, push hard now Nico” to which the championship leader replied: “Pushing hard is not the long game.” Precisely.

Mercedes were also going to bring Hamilton in for an early pit stop but changed their minds and brought Rosberg in instead, closely followed by Hamilton.

Nothing, however, could disrupt the composure of the world champion who produced one of his most commanding performances of the year at a time when knew he had to.

This was another showing of the summer form Hamilton displayed when he won six races out of seven. He made a second pit stop but at the end of the race his winning margin was 4.5sec.

It was a result that maintains interest in the destination of the world championship with three races to go, but to make it really compelling needs a non-finish by Rosberg.